Question 696996
Let the first AP is represented as TA = a1 + (n1-1)d , where a is the first term and d is the common difference , n1 is the number of terms in AP1.
Let the second AP be represented as TB = a2 + (n2-1)d.

Now ,

100th term of TA is TA100  = a1 + 99d
Similarly, 100th term of TB is TB100 = a2+99d

{{{TB100-TA100 = (a2-a1) = 100}}}

Therefore , {{{TA1000 - TB1000 = (a2+999d)-(a1+999d)}}}
The difference is {{{(a2-a1) = 100}}}